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A056642 Number of linear spaces on n (labeled) points. 9
1, 1, 2, 6, 32, 353, 8390, 433039, 50166354, 13480967630 (list; graph; refs; listen; history; text; internal format)



Alternatively, number of linear geometries on n (labeled) points. For the unlabeled case see A001200.

Also a(n) = 1 + number of simple rank-3 matroids on n (labeled) elements; a(n) = number of 2-partitions of a set of size n.


L. M. Batten and A. Beutelspacher: The theory of finite linear spaces, Cambridge Univ. Press, 1993 (see the Appendix).

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 303, #42.

J. Doyen, Sur le nombre d'espaces linéaires non isomorphes de n points, Bull. Soc. Math. Belg. 19 (1967), 421-437.

J. A. Thas, Sur le nombre d'espaces linéaires non isomorphes de n points, Bull. Soc. Math. Belg. 21 (1969), 57-66.


Table of n, a(n) for n=1..10.

W. M. B. Dukes, Tables of matroids.

W. M. B. Dukes, Counting and Probability in Matroid Theory, Ph.D. Thesis, Trinity College, Dublin, 2000.

W. M. Dukes, Bounds on the number of generalized partitions and some applications, Australas. J. Combin. 28 (2003), 257-261.

W. M. B. Dukes, On the number of matroids on a finite set, arXiv:math/0411557 [math.CO], 2004.

Index entries for sequences related to matroids


Corrected version of A001199. Cf. A002773, A001200, A031436, A058731.

Sequence in context: A005742 A055612 A236691 * A001199 A232469 A034997

Adjacent sequences:  A056639 A056640 A056641 * A056643 A056644 A056645




W. M. B. Dukes (dukes(AT)stp.dias.ie), Aug 28 2000


a(9) and a(10) from Gordon Royle, May 29 2006



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Last modified May 14 09:34 EDT 2021. Contains 343879 sequences. (Running on oeis4.)